New Methods in Iris Recognition John Daugman

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, VOL. 37, NO. 5, OCTOBER 2007 1167 New Methods in Iris Recognition John Daugman

Abstract—This paper presents the following four advances in presenting to the camera (e.g., nystagmus or deviated gaze). iris recognition: 1) more disciplined methods for detecting and The demands against false non-matches are also being raised faithfully modeling the iris inner and outer boundaries with active by the development of more tolerant and fluid user interfaces, contours, leading to more flexible embedded coordinate systems; 2) Fourier-based methods for solving problems in iris trigonome- which aim to replace the “stop-and-stare” camera interface with try and projective geometry, allowing off-axis gaze to be handled iris recognition on the move, off-axis, and at a distance [9]. by detecting it and “rotating” the eye into orthographic perspec- These two trends seem to require, paradoxically, that de- tive; 3) statistical inference methods for detecting and excluding cision criteria be used which are simultaneously much more eyelashes; and 4) exploration of score normalizations, depending conservative and liberal than those that are presently deployed. on the amount of iris data that is available in images and the required scale of database search. Statistical results are presented The purpose of this paper is to present four new advances in based on 200 billion iris cross-comparisons that were generated iris recognition that aim to simultaneously improve at both from 632 500 irises in the United Arab Emirates database to extremes. Sections II–IV present new methods of image analyze the normalization issues raised in different regions of processing for iris segmentation, allowing flexible shapes and receiver operating characteristic curves. coordinate systems. The images used in these sections come Index Terms—Active contours, biometrics, Gabor wavelets, from the National Institute of Standards and Technology gaze correction, iris recognition, score normalization, texture. (NIST) “Iris Challenge Evaluation” (ICE-1), and their file numbers are cited to facilitate comparative work. Sections V I. INTRODUCTION and VI analyze alternative score normalization rules that are adapted for differently sized databases, using results from HE ANTICIPATED large-scale applications of biometric 200 billion iris cross-comparisons. T technologies such as iris recognition are driving innovations at all levels, ranging from sensors to user interfaces, to algorithms and decision theory. At the same time as these II. ACTIVE CONTOURS AND GENERALIZED COORDINATES good innovations, possibly even outpacing them, the demands on the technology are getting greater. Today, many countries Iris recognition begins with finding an iris in an image, de- are considering or have even announced procurement of bio- marcating its inner and outer boundaries at the pupil and sclera, metrically enabled national identity (ID) card schemes, one of detecting the upper and lower eyelid boundaries if they occlude, whose purposes will be to detect and prevent multiple IDs. and detecting and excluding any superimposed eyelashes or Achieving that purpose will require, at least at the time when reflections from the cornea or eyeglasses. These processes may cards are issued and IDs are registered, an offline “each-against- collectively be called segmentation. Precision in assigning the all” cross-comparison. In effect then the number of biometric true inner and outer iris boundaries, even if they are partly comparisons that must be performed scales as the square of the invisible, is important because the mapping of the iris in a population. The decision confidence levels that will be required dimensionless (i.e., size invariant and pupil dilation invariant) to keep the false match rate (FMR) negligible, despite such vast coordinate system is critically dependent on this. Inaccuracy in numbers of opportunities to make false matches, can only be the detection, modeling, and representation of these boundaries described as astronomical. can cause different mappings of the iris pattern in its extracted At the other end of the conceptual receiver operating char- description, and such differences could cause failures to match. acteristic (ROC) curve from the FMR =0limit, much greater It is natural to start by thinking of the iris as an annulus. demands are also being placed on the false non-match rate Soon, one discovers that the inner and outer boundaries are (FnMR). This is partly because national-scale deployments usually not concentric. A simple solution is then to create must be as inclusive as possible; hence, it is unacceptable a nonconcentric pseudo-polar coordinate system for mapping to exclude members of outlier populations who, for various the iris, relaxing the assumption that the iris and pupil share reasons, may have a nonstandard eye appearance (e.g., non- a common center and requiring only that the pupil is fully round iris, coloboma, oddly shaped pupil, drooping eyelids, contained within the iris. This “doubly dimensionless pseudo- or much eyelash occlusion) or who simply have difficulty polar coordinate system” was the basis of my original paper on iris recognition [2] and patent [3], and this iris coordinate system was incorporated into International Organization for Standardization (ISO) Standard 19794-6 for iris data [7]. Soon Manuscript received September 20, 2006. This paper was recommended by one also discovers that, often, the pupil boundary is noncircular, Guest Editor K. W. Bowyer. and usually, the iris outer boundary is noncircular. Performance The author is with the Computer Laboratory, University of Cambridge, CB3 0FD Cambridge, U.K. in iris recognition is significantly improved by relaxing both Digital Object Identifier 10.1109/TSMCB.2007.903540 of those assumptions, replacing them with more disciplined

Fig. 1. Active contours enhance iris segmentation, because they allow for Fig. 2. Active contours enhance iris segmentation, because they allow for noncircular boundaries and enable flexible coordinate systems. The box in noncircular boundaries and enable flexible coordinate systems. The box in the lower left-hand corner shows curvature maps for the inner and outer iris the lower left-hand corner shows curvature maps for the inner and outer iris boundaries, which would be flat and straight if they were circles. Here, the outer boundaries, which would be flat and straight if boundaries were circles. Here, boundary (upper plot) is particularly noncircular. Dotted curves in the box and the pupil boundary (lower plot) is particularly noncircular. Dotted curves in the on the iris are Fourier series approximations. This iris is ICE-1 file 239261. box and on the iris are Fourier series approximations. This iris is ICE-1 file 240461. methods for faithfully detecting and modeling those boundaries whatever their shapes are and defining a more flexible and level for each snake is the image gradient in the radial direction. generalized coordinate system on their basis. Thus, the relative thickness of each snake roughly represents the Because the iris outer boundary is often partly occluded by sharpness of the corresponding radial edge. If an iris boundary eyelids, and the iris inner boundary may be partly occluded by were well-described as a circular edge, then the corresponding reflections from illumination, and sometimes both boundaries snake in its box should be flat and straight. In general, this is also by reflections from eyeglasses, it is necessary to fit flex- not the case. ible contours that can tolerate interruptions and continue their The dotted curve that is plotted within each snake, as well trajectory across them on a principled basis, which is somehow as superimposed on the corresponding loci of points in the iris driven by the data that exist elsewhere. A further constraint is image, is a discrete Fourier series approximation to the data. that both the inner and outer boundary models must form closed (In both figures, detected eyelid occlusions are also demarcated curves. A final goal is that we would like to impose a constraint by white pixels, and they interrupt the corresponding outer on smoothness based on the credibility of any evidence for boundary data snake, although the estimated contour continues nonsmooth curvature. through such interruptions.) The estimation procedure is to An excellent way to achieve all of these goals is to describe compute a Fourier expansion of the N regularly spaced angular the iris inner and outer boundaries in terms of “active contours” samples of radial gradient edge data {rθ} for θ =0 to θ = based on discrete Fourier series expansions of the contour N − 1.AsetofM discrete Fourier coefficients {Ck},fork =0 data. By employing Fourier components whose frequencies to k = M − 1, is computed from the data sequence {rθ} as are integer multiples of 1/(2π), closure, orthogonality, and follows: completeness are ensured. Selecting the number of frequency components allows control over the degree of smoothness N−1 −2πikθ/N that is imposed and over the fidelity of the approximation. In Ck = rθe . (1) essence, truncating the discrete Fourier series after a certain θ=0 number of terms amounts to low-pass filtering the boundary Note that the zeroth-order coefficient or “DC term” C0 curvature data in the active-contour model. extracts information about the average curvature of the (pupil These methods are illustrated in Figs. 1 and 2. The lower or outer iris) boundary, or in other words, about its radius when left-hand corner of each figure shows two “snakes,” each con- it is approximated as just a simple circle. sisting of a fuzzy ribbon-like data distribution and a dotted From these M discrete Fourier coefficients, an approxima- curve, which is a discrete Fourier series approximation to the tion to the corresponding iris boundary (now without inter- data, including continuation across gap interruptions. The lower ruptions and at a resolution determined by M) is obtained snake in each snake box is the curvature map for the pupil as the new sequence {Rθ} for θ =0to θ = N − 1, which is boundary, and the upper snake is the curvature map for the iris expressed as follows: outer boundary, with the endpoints joining up at the six o’clock position. The interruptions correspond to detected occlusions M−1 1 by eyelids, which are indicated by separate splines in both R = C e2πikθ/N . (2) θ N k images, or by specular reflections. The data plotted as the gray k=0 DAUGMAN: NEW METHODS IN IRIS RECOGNITION 1169

As is generally true of active-contour methods [1], [8], there III. FOURIER-BASED TRIGONOMETRY is a tradeoff between how precisely one wants the model to AND OFF-AXIS GAZE fit all the data (improved by increasing M) versus how much A limitation of current iris recognition cameras is that they one wishes to impose constraints such as keeping the model require an on-axis image of an eye, which is usually achieved simple and of low-dimensional curvature (achieved by reducing through what may be called a “stop-and-stare” interface, in M; e.g., M =1enforces a circular model). Thus, the number which a user must align her optical axis with the camera’s M of activated Fourier coefficients is a specification for the optical axis. This is not as flexible or fluid as it might be. degrees of freedom in the shape model. It has been found that Moreover, sometimes, the standard cameras acquire images for a good choice of M for capturing the true pupil boundary with which the on-axis assumption is not true. For example, the appropriate fidelity is M =17, whereas a good choice for the NIST iris images that were made available and used for testing iris outer boundary where the data is often much weaker is in ICE-1 contained several images with very deviated gaze, M =5. It is also useful to impose monotonically decreasing weights on the computed Fourier coefficients {C } as further probably because the user’s gaze was distracted by an adjacent k monitor. control on the resolution of the approximation {Rθ}≈{rθ}, which amounts to low-pass filtering the curvature map in its The on-axis requirement can be relaxed by correcting the Fourier representation. Altogether, these manipulations, partic- projective deformation of the iris when it is imaged off-axis, ularly the two different choices for M, implement the computer provided that one can reliably estimate the actual parameters of vision principle that strong data (the pupil boundary) may be gaze. Dorairaj et al. [5] approached this by seeking the gaze modeled with only weak constraints, whereas weak data (the parameters that optimize the value of an integro-differential outer boundary) should be modeled with strong constraints. operator [2], [4], which detects circular boundaries. The gaze The active-contour models for the inner and outer iris bound- parameters that we seek include two spherical angles for eye aries support an isometric mapping of the iris tissue between pose, but the projective geometry also depends on the distance them, regardless of the actual shapes of the contours. Suppose between the eye and the camera, which may be unknown, the contour model for the pupillary boundary consists of Carte- and on the surface curvature of the iris, which is generally not zero. If simplifying assumptions and approximations are sian coordinates (xp(θ),yp(θ)) with arc parameter θ ∈ [0, 2π] and the outer boundary of the iris at the sclera is described by made about the latter factors, then a simple affine projective transformation may suffice to make the iris recognizable against the contour model (xs(θ),ys(θ)). Then, a shape-flexible, size- invariant, and pupil-dilation-invariant dimensionless coordinate itself as imaged in other poses, orthographic or not. system for the iris portion of the image I(x, y) can be repre- The essence of the problem is then estimating the two angles sented by the following normalized mapping: of gaze relative to the camera. Eye morphology is so variable in terms of visible sclera and eyelid occlusion that it is unlikely that such factors could support robust estimation, at least when → I(x(r, θ),y(r, θ)) I(r, θ) (3) only one eye is imaged; although it must be noted that humans are very impressively skilled somehow at monitoring each where the dimensionless parameter r ∈ [0, 1] spans the unit other’s gaze direction. In the absence of solving that mystery, interval, and an obvious alternative approach would be to assume that an orthographic image of the iris should reveal a circular pupil; therefore, detecting ellipticity of the pupil indicates off-axis x(r, θ) x (θ) x (θ) 1 − r = p s . (4) image acquisition, and estimating the elongation and orienta- y(r, θ) yp(θ) ys(θ) r tion of that ellipse would yield the two parameters of gaze deviation, modulo π in direction. We present here a somewhat The execution time for the entire subroutine that fits active more robust variant of this idea, which does not assume that contours to both the inner and outer iris boundaries is just the true pupil’s shape is circular when orthographically viewed. 3.5 ms on a 3-GHz PC with optimized code. The benefit of the This method of estimating gaze (and, thus, correcting for off- new adaptive coordinate system based on the active contours axis imaging) uses a new approach that may be called “Fourier- may be gauged by the improvement that it offers in recognition based trigonometry.” performance on difficult image databases. The NIST ICE-1 iris The method arises from the observation that Fourier series database contains many difficult images, producing a high false expansions of the X and Y coordinates of the detected pupil reject rate (FRR), which degrades the equal error rate (EER). boundary contain shape distortion information that is related Algorithms that yielded an EER of 1% (i.e., EER =0.01) when to deviated gaze, within the relationships among the real and using enforced circular models improved tenfold to an EER of imaginary coefficients of the lowest frequency term of each of 0.1% (i.e., EER =0.0011) on the same database by adopting those series expansions. In the special case that the true pupil this active-contours approach instead. boundary when viewed orthographically is really a circle, this Because of the flexibility of this method and its ability to method reduces to the simpler “ellipticity” method outlined establish a continuous deformation mapping between arbitrary above. shapes, we may call this a “generalized embedded coordinate We begin by considering that simple special case of a circular system,” or perhaps, more evocatively, we may use the name pupil. Let X(t) and Y (t) be the parameterized coordinate “Faberge coordinates” [10]. vectors of the pupil boundary, so the range of t is from 0 to 1170 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, VOL. 37, NO. 5, OCTOBER 2007

2π in one cycle around this closed curve. Clearly, in the case of a circular pupil with radius A, which is origin centered for simplicity, these functions are just X(t)=A cos(t) and Y (t)=A sin(t). In the case of deviated gaze along a cardinal axis, and assuming that the camera distance is large compared with the iris diameter so there is simple foreshortening along the cardinal axis, these functions become X(t)=A cos(t) and Y (t)=B sin(t), where A = B. Finally, if the gaze deviation is not along a cardinal axis but rather in direction θ, then these functions take the more general conic form for an oriented ellipse, which is described as follows:

X(t)=[A cos2 θ+B sin2 θ]cos(t)+[(B−A)cosθ sin θ]sin(t) (5) Y(t)=[(B−A)cosθ sin θ]cos(t)+[B cos2 θ+A sin2 θ]sin(t). (6)

It is worth noting that the information that we seek about gaze deviation, namely, the direction and magnitude of the deviation, are contained in the form of Fourier coefficients on the harmonic functions cos(t) and sin(t) that represent in their linear combination the contour data X(t) and Y (t). Specifically, the lowest complex-valued coefficient in a Fourier series expansion of the empirical function X(t) contains as its real and imaginary parts the coefficients a and b, respectively, which specify the phase in (5) as follows:

a = A cos2 θ + B sin2 θ (7) b =(B − A)cosθ sin θ. (8)

Likewise, the lowest complex-valued coefficient in a Fourier series expansion of the empirical function Y (t) contains as its Fig. 3. Fourier-based trigonometry enables gaze estimation and transformation of an image of an eye with deviated gaze into one apparently looking real and imaginary parts the coefficients c and d, respectively, directly at the camera. Without this transformation, such images would fail to which specify the phase in (6) as follows: be matched. This iris is ICE-1 file 244858. − c =(B A)cosθ sin θ (9) and the magnitude of the gaze deviation in direction θ is d = B cos2 θ + A sin2 θ. (10) expressed not as an angle but as the projective aspect ratio γ = B/A, which gives the second affine transformation Thus, we can derive the gaze deviation parameters that we parameter as seek just by computing the relevant Fourier coefficients of the empirical contour functions X(t) and Y (t). This estimation (a + d) cos(2θ)+a − d γ = . (12) process is independent of the higher order Fourier coefficients (a + d) cos(2θ) − a + d that will exist when the pupil has a shape that is more complex and irregular than a circle. The method is not restricted to such By estimating these parameters, the “Fourier-based an assumption about a circular shape. trigonometry” allows the projective geometric deformation Algebraic manipulation extracts from the four empirical caused by the gaze deviation to be reversed by an affine Fourier coefficients a, b, c, and d the gaze deviation parameters transformation of the off-axis image. This is illustrated in that we need. It should be noted that although the right-hand Fig. 3, which shows image 244858 from the NIST ICE-1 sides of (8) and (9) above appear to be identical functions of the database in the upper panel and the same eye image after desired parameters, these equations express constraints based “correcting” the gaze deviation by an affine transformation on different empirical data. Quantities a and b are obtained from with the extracted parameters (θ, γ) in the lower panel. The X(t), whereas c and d are obtained from Y (t). The computed result of the transformation is to convert such images into direction of gaze deviation (modulo π) essentially has the form apparent orthographic form, appearing to rotate the eyes in of Fourier phase information, i.e., their sockets, making them recognizable against other images of the same eye. A limitation of this method is that the affine −b − c transformation assumes that the iris is planar, whereas, in fact, θ =0.5 arctan (11) a − d it has some curvature. DAUGMAN: NEW METHODS IN IRIS RECOGNITION 1171

the median of the mother distribution, thus confirming that not only are there two populations but also that they are sufficiently different from each, then the threshold is accepted, and pixels below it are deemed to arise from superimposed eyelashes. In the iris image itself in Fig. 4, these detected eyelashes within the iris have now been marked as white pixels. Their positions are recorded in a mask array that prevents them from influencing the data that encode the iris texture.

V. S CORE NORMALIZATIONS Iris recognition works by performing a test of statistical independence between two IrisCodes, in order to decide whether they arise from the same or from different irises [2]–[4]. This test of statistical independence is equivalent to tossing a coin many times, with each toss representing a comparison between Fig. 4. Statistical inference of eyelashes from the iris pixel histogram and two bits in the two IrisCodes, in order to decide whether or not determination of a threshold for excluding the lashes (labeled in white) from the coin is fair by delivering roughly 50–50 outcomes. If such a influencing the IrisCode. This iris is ICE-1 file 239766. result is obtained, then the irises can be judged as independent; but if there is a great preponderance of, e.g., “heads,” which IV. EXCLUDING EYELASHES BY STATISTICAL INFERENCE means that a large majority of corresponding bit pairs agreed, then that is strong evidence that the IrisCodes came from the One of the ways in which iris image data may be corrupted, same iris. But what is the effect of greatly varying numbers besides reflections, camera noise, and eyelid occlusion, is oc- of such “coin tosses” in these correlated Bernoulli trials, due clusion by eyelashes (usually from the upper eyelid). These to varying amounts of iris data being visible and available for often have random and complex shapes, combining with each comparison? other to form masses of intersecting elements rather than just Areas of the iris that are obscured by eyelids, eyelashes, simple hair-like strands that might be amenable to detection by or reflections from eyeglasses, or that have low contrast or a elementary shape models. They can be the strongest signals in low signal-to-noise ratio, are detected by the image-processing the iris image in terms of contrast or energy, and they could algorithms and prevented from influencing the iris comparisons dominate the IrisCode with spurious information if not detected through bitwise mask functions. Whereas the IrisCode bits and excluded from the encoded data. themselves contain phase data [2]–[4] that are XORed ( ) The inference of eyelashes and their exclusion from the to detect disagreement and thereby determine similarity be- IrisCode can be handled by statistical estimation methods that tween two irises, the bits to be considered are first selected by essentially depend on determining whether the distribution of ANDing ( ) each pair with the associated mask functions of iris pixels is multimodal. If the lower tail of the iris pixel both irises to ensure their validity and their significance. The histogram supports a hypothesis of multimodal mixing, then norms () of the resultant bit vector and of the ANDed mask an appropriate threshold can be computed, and pixels outside vectors are then measured in order to compute a raw Hamming it can be excluded from influencing the IrisCode. distance HDraw, as the fraction of meaningful bits that disagree Fig. 4 illustrates this method. The panel in its lower-right between two irises whose two phase code bit vectors are de- corner superimposes four histograms, all computed from just noted {codeA, codeB} and whose mask bit vectors are denoted the pixels in the segmented iris portion of the image between {maskA, maskB}.Thus,wehave the detected eyelids. The solid gray distribution is a histogram of all the iris pixels (ranging from 0 to 255). The two dotted (codeA codeB) maskA maskB HD = . (13) outline histograms break this up into two components, one for raw maskA maskB just the lower part of the iris (white dotted curve), and the other for just the upper part of the iris (black dotted curve). Usually, the total number of bit pairs that are available The solid black histogram is the difference between these for comparison, i.e., maskA maskB, is nearly a thousand. two histograms. We are interested in whether the cumulatives However, if one of the irises has, for example, almost complete from the left of this difference histogram pass a test of being occlusion of its upper half by a drooping upper eyelid, and statistically separable from the mother (solid gray) distribution. if the other iris that is being compared with it has almost If so, based on significant Z-score deviations between their complete occlusion of its lower half, then the common area respective quartiles, the hypothesis that the iris contains some available for comparison may be almost nil. In such cases, superimposed eyelash pixels may be accepted. returning to the coin-tossing analogy, our test for the “fairness” The vertical dashed line in the histogram panel indicates of the coin (i.e., statistical independence of the two IrisCodes by the computed threshold where such a hypothesis in this case finding a nearly 50–50 result) will be based upon a very small (for this image) is supported. If that hypothesis also passes a number of Bernoulli trials indeed. Therefore, the interpretation further test on the deviation between the threshold quartile and of any given deviation from the 50–50 outcome that is expected 1172 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, VOL. 37, NO. 5, OCTOBER 2007 for independence must take into account the total amount of comparison data that were available. This is the role of score normalization. A natural choice for the score normalization rule would be to rescale all deviations from a 0.5 raw Hamming distance in proportion to the square root of the number of bits that were compared when obtaining that score. The reason for such a rule is that the expected standard deviation in the distribution of Bernoulli trial outcomes (expressed as a fraction of the n Bernoulli trials having a given outcome) is σ =(pq/n)1/2, where p and q are the respective outcome probabilities (both nominally 0.5 in this case). Thus, decision confidence levels can be held constant, irrespective of how many bits n were actually compared, by mapping each raw Hamming distance HDraw into a normalized score HDnorm using a rescaling rule like n HD =0.5 − (0.5 − HD ) . (14) norm raw 911

This normalization should transform all samples of scores obtained when comparing different eyes into samples drawn from the same binomial distribution, whereas the raw scores HDraw might be samples from many different binomial distributions Fig. 5. Comparison of two algorithms on the NIST ICE-1 database: with having standard deviations σ that are dependent on the number and without score normalization (i.e., Algorithms 1 and 2, respectively). Solid of bits n that were actually available for comparison. This nor- squares mark their EER points. In this region of the ROC curve near EERs, malization maintains constant confidence levels for decisions where the required FMRs are not very demanding, best performance is achieved without score normalization. using a given Hamming distance threshold, regardless of the value of n. The scaling parameter 911 is the typical number of bits compared (unmasked) between two different irises, as However, in much more aggressive regions of the ROC, estimated from one particular (early) database. Today, based where one demands an FAR of perhaps one in a billion for on much larger databases, it appears that a better choice for applications such as national database search or “all-against- that parameter may be about 960. In any case, when comparing all” cross-comparisons over large databases to discover any different normalization rules in this paper, this rule (14) will be multiple IDs, the benefits of score normalization become ap- termed “SQRT normalization.” parent. It is informative to first examine what occurs in this The benefit of SQRT normalization is to prevent false region without score normalization. We must use a much larger matches arising by chance due to few bits being compared (just database than the released part of the NIST ICE-1 database, as few coin tosses may well yield all “heads”). However, the because the latter allows only a few million cross-comparisons cost of this normalization for n is that same-eye matches are between different eyes. We must explore the behavior when penalized when few bits are available for comparison; even many billions of cross-comparisons are done. This is possi- if they all agreed, so that HDraw =0, the resulting HDnorm ble with the United Arab Emirates (UAE) database of N = may be above the acceptance threshold, and the match would 632 500 IrisCodes all obtained from different eyes, enabling be rejected. This penalty is apparent by comparing false re- a total of N · (N − 1)/2 = 200 billion different pair compar- ject performance with and without score normalization on the isons. Based on this complete set of 2 × 1011 pairings, Table I NIST ICE-1 iris database, which consists of a few thousand shows the observed FMRs for unnormalized scores HDraw as a iris images that NIST released together with “ground-truth” function of both the decision threshold and the number of bits information. This image database contained many very difficult compared. and corrupted images, often in poor focus and with much eyelid It is clear from Table I that false matches are much more occlusion, and sometimes with the iris partly outside the image likely (at any Hamming distance criterion) when fewer bits frame. In the region of the receiver operating characteristic were the basis of the comparison. For example, at a criterion (ROC) curve [tradeoff between FRR and false accept rate of HDraw =0.285, using unnormalized scores, a false match (FAR)], where one tolerates rather high FAR such as one in would be 1000 times more likely when only 400 bits were 1000 or one in 10 000, as shown in Fig. 5, the cost of score the basis of the comparison than if 1000 bits were avail- normalization (Algorithm 1) on FRR is clear. The EER (where able for comparison. This illustrates the importance of score FRR = FAR) is about 0.001 without score normalization, but normalization. 0.002 with normalization. Similarly, at other nominal points of For the same UAE database, Fig. 6 compares the FMRs interest in this region of the ROC curve, as tabulated within for the three approaches to normalizing scores based on the Fig. 5, the cost of score normalization is roughly a doubling number of bits compared. The upper plot takes no account of in FRR. the number of bits, so it has the highest FMRs. (It should be DAUGMAN: NEW METHODS IN IRIS RECOGNITION 1173

TABLE I FMR WITHOUT SCORE NORMALIZATION:DEPENDENCE ON THE NUMBER OF BITS COMPARED AND THE CRITERION

Fig. 7. Distribution of HDnorm normalized similarity scores (14) for 200 billion different pairings of iris patterns, without relative rotations. The solid curve ﬁtting the histogram is a binomial density (15).

Fig. 6. Comparisons of three approaches to score normalization based on of the ROC curve and involving only a small database, best 200 billion iris cross-comparisons using the UAE database of 632 500 performance was achieved without score normalization because IrisCodes. FMRs are plotted in semilogarithmic coordinates versus decision that amounts to a penalty on good matches when few bits were criterion. The range of the ordinate in this plot spans a factor of 300 000 to 1. compared. However, in the vastly more demanding domain noted that, in Fig. 6, all iris comparisons were done in each of national-scale databases that involve possibly astronomical of several relative orientations to compensate for possible tilt, numbers of cross-comparisons, as investigated in Fig. 6 with making all FMRs about seven times worse than the case in 200 billion iris comparisons, normalizing scores by the number Table I because of the increased number of opportunities.) The of bits on which they were based is a critical necessity. bottom curve in Fig. 6 shows the beneﬁt of score normalization using the SQRT rule given in (14), causing the observed FMR to VI. ADAPTING FOR LARGE-SCALE DATABASES plummet to one in 200 billion at a criterion around HDnorm = 0.262. This performance is about 2000 times better than without Using the SQRT normalization rule, Fig. 7 presents a his- the normalization (note the semilogarithmic coordinates). The togram of all 200 billion cross-comparison similarity scores middle curve represents a hybrid normalization rule that is a among the 632 500 different irises in the UAE database. The linear combination of the other two, taking into account the vast majority of IrisCodes from different eyes disagreed in number of bits compared only when in a certain range. roughly 50% of their bits, as expected, since the bits are We learn from these comparisons of alternative normaliza- equiprobable and uncorrelated between different eyes [2], [4]. tion rules that performance in different regions of the ROC Very few pairings of IrisCodes could disagree in fewer than curve is optimized by different rules. In the relatively unde- 35% or more than 65% of their bits, as is evident from the manding domain highlighted in Fig. 5, near the EER point distribution. 1174 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, VOL. 37, NO. 5, OCTOBER 2007

The solid curve that ﬁts the data very closely in Fig. 7 is TABLE II a binomial probability density function. This theoretical form FMRs WITH HDnorm SCORE NORMALIZATION:DEPENDENCE ON THE CRITERION (200 BILLION COMPARISONS,UAEDATABASE) was chosen because comparisons between bits from different IrisCodes are Bernoulli trials, or conceptually “coin tosses,” and Bernoulli trials generate binomial distributions. If one tossed a coin whose probability of “heads” is p in a series of N independent tosses and counted the number m of “heads” outcomes, and if one tallied this fraction x = m/N in a large number of such repeated runs of N tosses, then the expected distribution of x would be as per the solid curve in Fig. 7. Thus, we have

N! f(x)= pm(1 − p)(N−m). (15) m!(N − m)!

The analogy between tossing coins and comparing bits between different IrisCodes is deep but imperfect, because any given IrisCode has internal correlations arising from iris fea- tures, especially in the radial direction [2]. Further correlations are introduced because the patterns are encoded using 2-D Gabor wavelet filters [4], whose low-pass aspect introduces correlations in amplitude, and whose bandpass aspect introduces correlations in phase, both of which linger to an extent that is inversely proportional to the filter bandwidth. The effect presented. Under the assumption of independence between the of these correlations is to reduce the value of the distribution right- and left-eye IrisCodes, which is strongly supported by the parameter N to a number that is significantly smaller than available data (see [4, Fig. 6]), the confidence levels in Table II the number of bits that are actually compared between two could be multiplied together for matches that were obtained IrisCodes; N becomes the number of effectively independent with both eyes. bit comparisons. The value of p is very close to 0.5 (empirically The requirements of biometric operation in the “identifi- 0.499 for the UAE database), because the states of each bit are cation” mode by exhaustively searching a large database are equiprobable apriori, and so any pair of bits from different vastly more demanding than merely operating in a one-to-one IrisCodes are equally likely to agree or disagree. “verification” mode (in which an ID must first be explicitly The binomial functional form that very well describes the asserted, which is then verified in a yes/no decision by com- distribution of normalized similarity scores for comparisons parison against just the single nominated template). between different iris patterns is the key to the robustness of If P1 is the false match probability for single one-to-one these algorithms in large-scale search applications. The tails verification trials, then (1 − P1) is the probability of not mak- of the binomial attenuate extremely rapidly, because of the ing a false match in single comparisons. The likelihood of dominating central tendency caused by the factorial terms in successfully avoiding this in each of N independent attempts N (15). Rapidly attenuating tails are critical for a biometric to is therefore (1 − P1) ; hence, PN , which is the probability survive the vast numbers of opportunities to make false matches of making at least one false match when searching a database without actually making any, when applied in an “all-against- containing N different patterns, is given by all” mode of searching for matching or multiple IDs, as con- N templated in some national ID card projects in the U.K. and PN =1− (1 − P1) . (16) elsewhere in Europe. The cumulatives (up to various thresholds) under the left tail By observing the approximation that PN ≈ NP1 for small of the distribution of normalized similarity scores for different P1 1/N 1, when searching a database of size N,an irises compared at multiple relative tilts reveal the FMRs among identifier needs to be roughly N times better than a verifier the 200 billion iris comparisons if the identification decision to achieve comparable odds against making false matches. In policy used those thresholds. These rates are provided in effect, as the database grows larger and larger, the chance of Table II. Although the smallest observed match was around making a false match also grows almost in proportion. These 0.26, the table has been extended down to 0.22 using the theo- chances also grow in proportion to the number of independent retical cumulative of the extreme value distribution of multiple searches that are conducted against the database. To success- samples from the binomial (15) plotted as the solid curve in fully survive so many opportunities to make false matches, the Fig. 5 in order to extrapolate the theoretically expected FMRs decision threshold policy must be adaptive to both of these for such decision policies. These FMRs, whether observed or factors. Fortunately, because of the underlying binomial com- theoretical, also serve as confidence levels that can be associ- binatorics, the algorithms with score normalization generate ated with a given quality of match using the score normalization extremely rapidly attenuating tails for the HDnorm distribution. rule (14). In this analysis, only a single eye is presumed to be This felicitous property enables very large databases to be DAUGMAN: NEW METHODS IN IRIS RECOGNITION 1175

accommodated and large numbers of searches to be conducted [4] J. G. Daugman, “How iris recognition works,” IEEE Trans. Circuits Syst. against them. The rule to be followed for decision policy thresh- Video Technol., vol. 14, no. 1, pp. 21–30, Jan. 2004. [5] V. Dorairaj, N. Schmid, and G. Fahmy, “Performance evaluation of non- old selection is to multiply the size of the enrolled database ideal iris based recognition system implementing global ICA encoding,” times the number of searches to be conducted against it in a in Proc. IEEE ICIP, 2005, vol. 3, pp. 285–288. given interval of time and then to determine from Table II what [6] F. Hao, J. G. Daugman, and P. Zielinski, “A fast search algorithm for a large fuzzy database,” IEEE Trans. Inf. Forensics Security, 2007. Hamming distance threshold will correspond to the risk level [7] Information Technology—Biometric Data Interchange Formats, Part 6: that is deemed to be acceptable. Again, Table II assumes that Iris Image Data, 2005. ISO/IEC Standard 19794-6. only a single eye is used for matching. [8] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Active contour models,” Int. J. Comput. Vis., vol. 1, no. 4, pp. 321–331, 1988. For example, in the U.K., with a national adult population of [9] J. Matey, K. Hanna, R. Kolcyznski, D. LoIacono, S. Mangru, about 45 million, an “all-against-all” comparison of IrisCodes, O. Naroditsky, M. Tinker, T. Zappia, and W-Y. Zhao, “Iris on the move: which totals to about 1015 pairings, as envisioned to search Acquisition of images for iris recognition in less constrained Environ- ments,” Proc. IEEE, vol. 94, no. 11, pp. 1936–1947, Nov. 2006. for any multiple IDs when issuing the proposed biometric ID [10] Website about generalized Faberge embeddings. [Online]. Available: cards, could be performed using an HDnorm decision threshold http://users.vnet.net/schulman/Faberge/eggs.html as high as 0.22 without expecting to make any false matches. At this threshold, in order to keep the FnMR acceptably low (e.g., below 1%), systems will need to be more tolerant than the currently deployed ones in order to handle difficult image John Daugman received the A.B. and Ph.D. degrees capture conditions, or unusual eyes and nonideal presentations. from Harvard University, Cambridge, MA. It is hoped that the new image-processing algorithms intro- He was with the faculty of Harvard University duced in Sections II–IV of this paper using active contours, before he joined Cambridge University, Cambridge, U.K., in 1991, where he is currently with the Com- deviated gaze correction, and other improvements can help in puter Laboratory. He has held visiting Professor- achieving those requirements. A further advance that allows ships at the University of Groningen, Groningen, The IrisCodes to be indexed by their collisions with substrings, Netherlands, as the Johann Bernoulli Chair of Math- ematics and Informatics, and at the Tokyo Institute of thereby replacing the need for exhaustive search (which is time Technology, Tokyo, Japan, as the Toshiba Endowed consuming in large databases) by instead almost instantaneous Chair. His areas of research and teaching are com- direct addressing with IrisCodes, is the subject of a separate puter vision and biological vision, pattern recognition, information theory, and neural computing. He is the inventor of iris recognition, and his algorithms paper [6]. currently underlie all public deployments of this technology worldwide. He serves or has served as an Associate Editor of Network: Computation in Neural Systems International Journal of Wavelets, Multiresolution, and Informa- REFERENCES ,the tion Processing, Cognitive Brain Research,andtheJournal of Computation and [1] A. Blake and M. Isard, Active Contours. Heidelberg, Germany: Mathematics. Springer-Verlag, 1998. Dr. Daugman has served as an Associate Editor of the IEEE TRANSACTIONS [2] J. G. Daugman, “High confidence visual recognition of persons by a test of ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE. He received the U.S. statistical independence,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 15, Presidential Young Investigator Award from the National Science Foundation, no. 11, pp. 1148–1161, Nov. 1993. the Information Technology Award and Medal from the British Computer [3] J. G. Daugman, “Biometric personal identification system based on Society, the “Millennium Product” Award from the U.K. Design Council, the iris analysis,” U.S. Patent 5,291,560, Mar. 1, 1994. U.S. Pat. Off., Smithsonian and “Time 100” Innovators Award (U.S.), and the OBE, Order of Washington, DC. the British Empire, for his scientific and technical work.